Week+3

Lesson: Primes and Composites
This week, we begin by looking at prime and composite numbers. We'll listen to Khan define prime numbers for us here

And we'll get a chance to see if we got the idea by practicing here

Defining a prime number is easy. Figuring out what they are is a little harder. This video will show you an ancient method for determining prime numbers:

media type="custom" key="23768152" Determining which numbers are composite numbers is a bit easier. A composite is any number (besides 1) that isn't prime. In other words, it has factors besides 1 and itself.

Now that we watched the video, let's get involved with Eratosthenes' idea and see how he used his famous "sieve" to remove numbers that weren't primes from his list. Here's one place to do that: Sieve of Eratosthenes.

Lesson: Rules of Divisibility
Number Sense techniques make mathematics much easier, fun, and even awe-inspiring. If you don't believe that, watch this. media type="custom" key="23789784" align="left"

**The Mathemagician**

While very few will ever match the ability of Dr. Benjamin, Number Sense techniques will help all of us in our everyday activities.

Let's start with the basics: The Rules of Divisibility. Knowing how to factor a number is an important skill in mathematics. Without it, we can't even add fractions unless their denominators are the same.

Here's a table of some basic divisibility rules you'll find indispensable. They are Number Sense techniques that make many tasks easier -- and sometimes faster to do by hand than with a calculator. It's nice to have a few tricks up our sleeve to make our lives easier. You should try to memorize these rules.

Ex: “111” 1+1+1 = 3 so 111 is divisible by three. || Ex: “249764” 64 is divisible by 4 so 249764 is divisible by 4. || Ex: “702” It is even and 7+0+2 = 9 so it’s divisible by 3. || Ex: “203” 203 → 20 – 2(3) = 14  || Ex: “648” 6 is even and 48 is divisible by 8 so 648 is divisible by 8. Ex: “298160” 1 is odd and 60 – 4 = 56 which is divisible by 8 so 298160 is divisible by 8. || Ex: “2151” 2+1+5+1 = 9 so 2151 is divisible by 9. || Ex. “5014856” → 5 – 0 + 1 – 4 + 8 – 5 + 6 = 11 so 5014856 is divisible by 11. || If you want to download a copy, click here: .
 * Number || Rule ||
 * 2 || if the units digit is even (0, 2, 4, 6, or 8). ||
 * 3 || if the sum of the digits is a multiple of 3.
 * 4 || if the last two digits are divisible by 4.
 * 5 || if the units digit is 0 or 5. ||
 * 6 || if the number is both divisible by 2 and 3.
 * 7 || if the difference of twice the ones digit and the remaining digits is divisible by 7.
 * 8 || if 3 rd digit is odd and last two are divisible by 4; if 3 rd digit is even and last two are divisible by 8.
 * 9 || if the sum of the digits is a multiple of 9.
 * 10 || if the units digit is 0. ||
 * 11 || if the difference between the sum of evenly placed digits and oddly placed digits is 0 or a multiple of 11.
 * 12 || if the digit sum is divisible by three and the last two digits are divisible by 4. ||

Here's are a couple of screencasts to show how to use them.
 * Rules 1 through 7
 * Rules 8 through 12

We'll introduce more Number Sense techniques -- and regularly -- throughout the course. For now, let's practice what we've seen. Download the practice sheet below and see how well you do. We'll grade it in class.